The purpose of the investigation is to improve upon the widely used modified Fibonacci search scheme for dose escalation in Phase I clinical trials. The investigator will develop alternative dose escalation schemes and will compare these to the modified Fibonacci scheme and to other proposed schemes for dose escalation. Comparisons will be made using the methods of statistical decision theory and, where appropriate, will involve computer simulation studies. Of particular interest is the efficiency of the modified Fibonacci scheme relative to alternative schemes when the assumptions on which the modified Fibonacci are based are not satisfied.